Nonmagnetic In Substituted CuFe1âxInxS2 Solid Solution

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On the Non-Magnetic In Substituted CuFe1xInxS2 Solid Solution Thermoelectric Hongyao Xie, Xianli Su, Gang Zheng, Yonggao Yan, Wei Liu, Hao Tang, Mercouri G. Kanatzidis, Ctirad Uher, and Xinfeng Tang J. Phys. Chem. C, Just Accepted Manuscript • DOI: 10.1021/acs.jpcc.6b10308 • Publication Date (Web): 22 Nov 2016 Downloaded from http://pubs.acs.org on November 24, 2016

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The Journal of Physical Chemistry

On the Non-magnetic In Substituted CuFe1-xInxS2 Solid Solution Thermoelectric Hongyao Xie1, Xianli Su1*, Gang Zheng1, Yonggao Yan1, Wei Liu1, Hao Tang1, Mercouri G. Kanatzidis2, Ctirad Uher3 and Xinfeng Tang1* 1

State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China E-mail:[email protected]; [email protected] 2 Department of Chemistry, Northwestern University, Evanston, Illinois 60208, USA 3 Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA Abstract CuFeS2 is an environmentally friendly n-type thermoelectric material composed of earth-abundant, inexpensive and non-toxic elements. However, its rather undistinguished electronic properties combined with a high thermal conductivity lead to a low thermoelectric performance. In this work, an attempt is made to reduce the lattice thermal conductivity of CuFeS2 by In substituting on the Fe site. A series of CuFe1-xInxS2 (x=0~0.08) compounds was synthesized by vacuum melting combined with the plasma activated sintering (PAS) process, and the effect of substituting In atoms on the band structure and thermoelectric properties of CuFeS2 has been investigated. The results show that, the solubility limit of In in CuFeS2 is more than 8%. For the In content of 0.08, the lattice thermal conductivity of room temperature and at 630K was reduced by 60% and 37%, respectively, indicating that substituting In for Fe is an effective method to reduce the lattice thermal conductivity of CuFeS2. A single parabolic band model was used to calculate the effective mass of all samples, and the data indicate that small amounts of In do not change the band structure of CuFeS2. Finally, the thermoelectric performance have been enhanced due to the large decrease in lattice thermal conductivity. 1

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1 Introduction In the past decade, the energy crisis and environmental concerns have drawn much attention world-wide. Due to the ability to convert waste industrial heat directly into electricity, thermoelectricity has a considerable potential to contribute to a sustainable energy solution.1-5 The conversion efficiency of a thermoelectric material is determined by its dimensionless figure of merit defined as ZT=α2σT /(κe+κL) , where α, σ, T, κe and κL,are the Seebeck coefficient, electrical conductivity, absolute temperature, electronic thermal conductivity and lattice thermal conductivity, respectively.6-8 In order to achieve a high thermoelectric performance, the material should possess a large Seebeck coefficient, high electrical conductivity and a low lattice thermal conductivity. Although several excellent thermoelectric materials have been developed, such as Bi2Te3,9-11 CoSb3,12-14 PbTe,15-17 SnTe18-19 and GeTe compounds,20-21 their large-scale industrial applications have not yet materialized because most of them consist of toxic, low-abundant and therefore expensive elements. Consequently, it is very important to identify and develop alternative thermoelectric materials that use readily available, environmentally friendly and inexpensive elements, yet have even better thermoelectric performance. The diamond-like CuFeS2 compound, consisting of earth-abundant, low-cost and non-toxic elements has been considered as a potential thermoelectric material for intermediate temperature applications.22-24 Because of its intrinsic S vacancy defect, CuFeS2 shows an n-type semiconducting character with the band gap of 0.53 eV determined by optical absorption measurements25-26 and the Seebeck coefficient of -480 µV/K at room temperature.27-28 Thermoelectric properties are often judged and evaluated based on of the fundamental transport parameters in the expression (µ/κL)(m*/m0)3/2.9, 29 where µ is the carrier mobility, m* the effective carrier mass, mo the mass of an electron and κL the lattice thermal conductivity. Strong ionic 2


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bonding and a local magnetic moment carried by the Fe3+ ion scatter electrons very effectively, leading to a very low mobility and a low electrical conductivity.22, 27 In addition, on account of the constituent light elements and the character of its chalcopyrite structure, the intrinsic lattice thermal conductivity of CuFeS2 is very high, perhaps as much as 10 Wm-1K-1 at room temperature.22 All these features contribute to the low thermoelectric performance of CuFeS2. Hence, simultaneously increasing the carrier mobility and reducing the lattice thermal conductivity is of critical importance to improve the thermoelectric performance of CuFeS2. To improve the electrical conductivity of CuFeS2, most studies have focused on increasing the carrier concentration by introducing S deficiency,23 or doping with Zn,22, 30 Fe27, 31 or Co32. Although such efforts have improved the thermoelectric performance of CuFeS2, the results are still far off the mark needed to make CuFeS2 a competitive thermoelectric material. CuInS2 possesses the same chalcopyrite crystal structure as CuFeS2, Figure 1, and can be considered as a double sphalerite cell with the S atom residing in the tetrahedral void formed by the cationic elements.33 The solubility limit of CuInS2 in the CuFeS2 have been studied.34 In addition, compared with the Fe3+ ion, In is a non-magnetic element, and is an iso-valent substitution that should weaken magnetic scattering of the charge carriers. Furthermore, the In atoms possess a larger atomic mass and radius than the atoms of Fe, inducing mass and strain field fluctuation scattering in CuFeS2. This should reduce the thermal conductivity more effectively than Fe or Co doping on the Cu site. Thus, with In substituting on Fe sites , it should be possible to achieve a higher value of (µ/κL)(m*/m0)3/2, resulting in a high thermoelectric performance. In this work, a series of CuFe1-xInxS2 (x=0~0.08) compounds were synthesized by vacuum melting combined with the plasma activated sintering (PAS) process, and the effect of In 3



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substitutions on the band structure and thermoelectric properties of CuFe1-xInxS2 was investigated. We find that In substitution is very effective in reducing the lattice thermal conductivity of CuFeS2. For the sample with In content of x = 0.08, the lattice thermal conductivity at room temperature and at 630K was reduced by 60% and 37%, respectively. Calculations based on the Callaway model suggest that the mass and strain field fluctuation scattering in CuFeS2 is enhanced with In substitution. Estimates of the carrier effective mass indicate that small amounts of In do not substantially modify the band structure. Although the presence of In introduces alloy scattering for charge carriers and decreases their carrier mobility, the reduction of the thermal conductivity in conjunction with the likely weakened magnetic scattering is more dominant and lead to a larger value of (µ/κL)(m*/m0)3/2. The highest ZT of 0.17 is achieved at 630 K for CuFe0.96In0.04S2 and represents about a 30% enhancement over the ZT value of a pristine CuFeS2 sample.

2 Experimental Section High purity elements Cu (pieces, 99.99%), Fe (shot, 99.99%), In (pellet, 99.99%) and S (pieces, 99.99%) were weighed and mixed according to the nominal composition of CuFe1-xInxS2 (x=0, 0.02, 0.04 and 0.08). Stoichiometric quantities of the elements were sealed in evacuated quartz tubes and slowly heated up to 1323 K and held at this temperature for 24 h, followed by a slow furnace cooling down to a room temperature. The obtained ingots were hand-ground into fine powders using a mortar and a pestle. The powder was then sintered by plasma activated sintering (PAS) at 823 K under a pressure of 40 MPa in a vacuum to obtain fully-densified bulk samples. The phase structure of samples was examined by powder X-ray diffraction analysis (XRD; PANalytical–Empyrean，CuKα). The morphology of the bulk samples was characterized by field 4


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emission scanning electron microscopy (FESEM; Hitachi SU8020). The chemical composition was obtained by an energy dispersive spectrometer (EDS; JXA-8230/INCAX-ACT). The electrical conductivity and the Seebeck coefficient were measured at the same time by the ZEM-3 (Ulvac Riko, Inc) apparatus under a helium atmosphere from 300 to 630 K. The thermal conductivity was calculated according to the relationship κ =DCpρ, where D, Cp and ρ are thermal diffusivity, the heat capacity and the density of bulk samples, respectively. The thermal diffusivity (D) was measured using the laser flash system (LFA 457; Netzsch) in an argon atmosphere. The heat capacity (Cp) was determined by differential scanning calorimetry (DSC Q20; TA instrument) and the sample density (ρ) was specified by the Archimedes method. Below room temperature, the electrical conductivity and the Hall coefficient were measured in a Physical Property Measurement System (PPMS-9: Quantum Design) from 10 to 300 K under vacuum. The carrier concentration (n) and the carrier mobility (µH) were calculated according to equations: n = 1/eRH and µH = σ/ne.

3 Results and Discussion 3.1 Structural and Compositional Characterization Figure 2(a) shows the powder X-ray diffraction patterns for CuFe1-xInxS2 samples. All diffraction peaks in the XRD patterns can be indexed to the standard pattern of CuFeS2 (JCPDS#00-035-0752), indicating that all samples are single phases with the crystal structure of the CuFeS2 compound. Figure 2(b) shows the lattice parameters of CuFe1-xInxS2 samples as a function of the In content at room temperature. The lattice parameter increases with increasing content of In because the covalent radius of In is larger than that of Fe. Straight lines in Fig. 2(b) document a successful entry of In on the sites of Fe in the structure of CuFeS2 and the validity of 5



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the Vegard’s law. Microstructures on the fracture surfaces of all sintered samples were observed by FESEM. Because the morphologies of all samples are very similar, the CuFe0.92In0.08S2 compound is chosen as an example in Figures 3(a) and 3(b). The sintered samples are fully dense with a relative density above 98%. The character of the fracture is a trans-crystalline rupture. No obvious grains and grain boundaries are observed, indicating that In substitutions do not introduce any nanostructure in the CuFeS2 matrix. Figures 3(c) and 3(d) show back scattered electron images (BEI) of a polished surface and the elements distribution maps obtained by EDS on CuFe0.92In0.08S2. No impurity phase is detected.

All elements (Cu, Fe, In and S) are

homogeneously distributed on a micron scale. The XRD and EPMA results indicate that In successfully substitutes on the site of Fe in CuFeS2, and the structure can accommodate at least 8% of In without a trace of any secondary phase. The actual composition of all samples determined by EDS measurements is presented in Table 1.

3.2 Transport Properties The actual chemical compositions and the room temperature transport properties of CuFe1-xInxS2 samples are summarized in Table 1. The temperature dependence of electronic transport properties is discussed in sections 3.2.1 and thermal transport properties are the topic of section 3.2.2.

3.2.1 Electronic Transport Properties Temperature dependence of the electrical conductivity of CuFe1-xInxS2 samples as well as dependence on the content of In is shown in Figure 4(a). With the increasing content of In

6


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dopant, the electrical conductivity decreases in the entire temperature range. Specifically, the room temperature electrical conductivity decreases significantly from 5262 Sm-1 to 1790 Sm-1 for the sample of CuFe1-xInxS2 with x = 0.08. At lower temperatures, from 300 K to about 500 K, the electrical conductivity increases, particularly for the doped structures. This trend is reversed above 500 K and the conductivity then decreases. The initial rise in the electrical conductivity is due to a strongly rising density of carriers. Between 10K and 300 K, the electron carrier concentration of pristine CuFeS2 varies from 4.2 × 1016 cm-3 to 3.2 × 1019 cm-3 and the temperature dependence of the In doped samples is nearly similar, see Figure 5(a). The rising carrier density with temperature indicates a distinctly semiconducting behaviour. In CuFeS2, and presumably also for the range of In doping used here, d-orbitals of Fe hybridize with s-orbitals and p-orbitals of S, giving rise to an additional conduction band within the broad energy gap and this leads to the increased carrier concentration as temperature increases.35-36 The content of In itself has a rather weak influence on the electron density, as one would expect given that trivalent In substitutes for trivalent Fe. The only difference is that d-orbitals of Fe contribute to the density of electrons and thus In-doped samples have a marginally smaller carrier concentration. In any case, the rising carrier density with temperature indicates a distinctly semiconducting character of transport in all samples. The turn-around in the electrical conductivity above about 500 K is due to a rapidly decreasing electron mobility governed by electron scattering on acoustic phonons, see Figure 5(b), which overwhelms any further rise in the carrier concentration. Thus, according to the relationship σ = neµH, the behavior of the electrical conductivity reflects the combined influence of the carrier concentration and the carrier mobility. The Seebeck coefficient of CuFe1-xInxS2 samples and its temperature dependence is shown in Figure 4(b). All samples exhibit negative Seebeck coefficients over the entire temperature 7



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range, documenting the dominant n-type nature of transport in accord with the Hall measurement. The temperature dependent Seebeck coefficient follows the usual inverse relationship with respect to the temperature dependence of the electrical conductivity. Thus, in the temperature range extending to about 450 K, the magnitude of the Seebeck coefficient decreases while above 450 K it increases. Samples with the In content of x = 0.02 and x = 0.04, show a slightly diminished magnitude of the Seebeck coefficient in comparison to the pristine CuFeS2 sample. In contrast, the sample with the highest In content, x = 0.08, has a distinctly higher magnitude of the Seebeck coefficient than the pristine CuFeS2 sample up to nearly 600 K. The trend in the electrical conductivity and the Seebeck coefficient is reflected in the temperature and doping dependence of the power factor α2σ displayed in Figure 4(c). The Fermi level position and any variation in the band structure can be roughly deduced from the behavior of the electron effective mass. In order to further understand the effect of In substitution on the band structure, we estimate electron effective masses by using a single parabolic band model and assuming that scattering is dominated by acoustic phonons (confirmed by the temperature dependence of the carrier mobility). Then, combining the expressions for the Seebeck coefficient and the carrier concentration,

α=

 k B  ( r + 5 2 ) Fr +3 2 (η ) −η    e  ( r + 3 2 ) Fr +1 2 (η ) 

(1)

4π ( 2m ∗ k BT ) n= h3

(2)

32

F1 2 (η )

the effective mass can be calculated from the respective experimental values at 300 K. In Eqs. 1 and 2, α is the Seebeck coefficient, kB is the Boltzmann constant, r is a scattering parameter related to the energy dependence of the carrier scattering mechanism (here taken as r = -1/2, reflecting the dominance of acoustic phonon scattering), η is the reduced Fermi energy, h is the 8


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Planck constant, e is the electron charge, n is the carrier concentration, and m* is the effective mass.37-38 The results are presented in Table 1. Upon the presence of In in the structure, the effective mass of all CuFe1-xInxS2 compounds decreases from 2.2 to about 2, but this 10% decrease seems to be independent of a specific value of x. Thus, In substitutions at a level of up to 8% do not modify the band structure of CuFeS2 in any significant way. The Pisarenko relation, i.e., a plot of the Seebeck coefficient as a function of the carrier concentration at room temperature (assuming a parabolic band and an acoustic phonon scattering mechanism), gives a good description of the experimental results, as shown in Figure 6(a). All In substituted samples fall on the same line with the effective mass of 1.95 m0. No particular enhancement of the Seebeck coefficient by the resonant-state scattering mechanism nor some other effects are observed after In substitutes on the Fe site. Figure 6(b) depicts the room temperature power factor dependence on the carrier concentration for our CuFe1-xInxS2 compounds and the literature data22,

27

obtained on the

CuFeS2-based material. The dashed curve indicates that the optimum carrier concentration for CuFeS2 falls in the range between 1 to 2×1020cm-3, the range of concentrations for which the sample should achieve the highest power factor. As is apparent from the figure, the carrier concentration of our samples is in the range between 3 to 4×1019cm-3 and therefore falls far below the optimum value. This indicates that electronic properties of CuFe1-xInxS2 could be further improved by introducing a different donor able to increase the carrier concentration to the optimum value. In order to clarify the impact of magnetic scattering carried by Fe3+ and the role of In on the carrier mobility of CuFe1-xInxS2 compounds, the relationship between the alloying content and carrier mobility for CuFeS2 compounds with different dopants (In, Zn, Fe) is shown in 9



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Figure7(a). The chalcopyrite compound was loaded with different dopants to modulate the content of Fe3+, i.e, we synthesized composition of Cu1-xFe1+xS2 and Cu1-xZnxFeS2 (x = 0.01, 0.02, 0.03, 0.04, 0.05) and measured their carrier mobility. Figure7(a) displays the room temperature carrier mobility dependence on the alloying content for these compounds, the magnetic moment of different ions also show in the figure. First, for the sample with the same alloying content, the carrier mobility of CuFe1-xInxS2 compounds are higher than that of Cu1-xZnxFeS2 and Cu1-xFe1+xS2, and the Fe doping sample possess the lowest carrier mobility. Although the carrier concentration of all samples are not in the same level, an obvious correlation between the carrier mobility and the Fe3+ content have been noticed: When the dopant change from Fe to In, the Fe3+ content decrease (the Fe3+ content of Cu1-xFe1+xS2 is 1+x, for Cu1-xZnxFeS2 that is 1, while for CuFe1-xInxS2 that is 1-x) while the carrier mobility increase, thus In substituted samples possessed the highest carrier mobility among those compounds with the same doping content. It indicates In doping probably can weaken the magnetic scattering carried by Fe3+ in chalcopyrite. However, we have to acknowledge that it is very difficult to quantify intensity of the magnetic scattering carried by Fe3+ in chalcopyrite. Since there is a mixed scattering mechanisms affecting the carrier mobility at the same time. The calculated value (µ/κL)(m*/m0)3/2 of CuFe1-xInxS2 at room temperature, which is proportional to the TE efficiency, is depicted in Figure7(b). With increasing In content, the term (µ/κL)(m*/m0)3/2 increases except for the x=0.08 sample. Because In possess the higher atomic mass and radius than that of the Fe, it will increase the alloy scattering and scatter the phonon more effectively. In addition, as a kind of non-magnetic atom, In substitution may weaken the magnetic scattering of electron, which leads to a higher value of (µ/κL)(m*/m0)3/2, this indicated In substitution is effective to reduce the lattice thermal conductivity and also maintain the electron mobility. 10


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3.2.2 Thermal Conductivity and Figure of Merit ZT Temperature dependence of the total thermal conductivity of CuFe1-xInxS2 samples is shown in Figure 8(a). As the temperature increases, the thermal conductivity of all samples decreases on account of the enhanced Umklapp phonon scattering. Because the bipolar thermal conductivity contribution is small within the investigated temperature range, we can estimate the lattice thermal conductivity by subtracting the electronic thermal conductivity from the measured total thermal conductivity:

κ L = κ − κ e = κ − Lσ T

(3)

Here, κL is the lattice thermal conductivity, κ is the total thermal conductivity, and κe is the electronic thermal conductivity. The latter can be estimated by the Wiedemann-Franz relation, κe = LσT, where σ is the electrical conductivity and L is the Lorenz number.6 Assuming a single parabolic band model and acoustic phonon scattering, the Lorenz number L can be calculated by 39-40

2 2   k B   ( r + 7 2 ) Fr +5 2 ( η )  ( r + 5 2 ) Fr +3 2 ( η )   L=  −   e   ( r + 3 2 ) Fr +1 2 ( η )  ( r + 3 2 ) Fr +1 2 ( η )    

(4)

where, kB is the Boltzmann constant, e is the electron charge, r is the scattering factor (here again r = -1/2), η is the reduced Fermi energy, and Fn(η) is the Fermi integral defined as ∞

Fn (η ) = ∫ 0

χn 1 + e χ −η

dχ

(5)

With the Lorenz number thus calculated, the lattice thermal conductivity is shown in Figure

8(b). The room temperature lattice thermal conductivity of pure CuFeS2 is high, at 8.42 Wm-1K-1 but, as the content of In increases, it decreases rapidly to 3.45 Wm-1K-1 for CuFe0.92In0.08S2. At 630K these values are 2.33 and 1.47 Wm-1K-1 for CuFeS2 and CuFe0.92In0.08S2, respectively The large drop in the lattice thermal conductivity upon In doping is due to enhanced mass and strain 11



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field fluctuation scattering. From this perspective, In is an effective dopant. To ascertain how much further can the lattice thermal conductivity of CuFeS2 be reduced, a comparison is made with the minimum thermal conductivity of CuFeS2 calculated using the model proposed by Cahill, 41 13

κ min

T  π  =   k B na 2 3 ∑vi   6 i  θi 

2

∫

θi T

0

x3e x

( e x − 1)

2

dx

(6)

The model assumes the material has a completely disordered structure with na atoms per unit volume and the sound velocity vi. The sum in Eq. 6 is taken over three phonon modes of CuFeS2, one longitudinal and two transverse, with the velocities of vl = 3764 m/s and vs = 2056 m/s).27 θi is the cut-off frequency of mode i expressed as 13  h  2  ( 6π na )  kB 

θi = vi 

(7)

where, h is the Plank constant. The minimum thermal conductivity of CuFeS2 is shown in Figure

8(b) by a dashed line and stands at about 0.61 Wm-1K-1. Although the lattice thermal conductivity of CuFeS2 has been reduced to 1.47 Wm-1K-1 at 630K by 8% In substitution, this value is still more than twice the value of κmin, implying that the lattice thermal conductivity of CuFeS2 can be decreased further. In future studies, a synergistic combination of doping, forming solid solutions, and introducing nanostructures should be an effective strategy to decrease the lattice thermal conductivity and improve the thermoelectric performance further. We have noted that mass defect and strain field fluctuations are the reason why In doping is able to reduce the lattice thermal conductivity of CuFeS2. Is it the mass difference between In and Fe or the strain field created when larger In substitutes for Fe more effective in phonon scattering? In order to resolve the issue, the Callaway model is used to analyse the lattice thermal conductivity of CuFe1-xInxS2 compounds. 12


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Provided grain structures of all samples are similar and scattering from interfaces is the same, the only difference between the samples is the strength of Umklapp scattering and the density of point defects. Thus, the relation between the lattice thermal conductivity of the doped CuFe1-xInxS2 (κL) and that of the pure CuFeS2 compound (κLP) can be expressed as:42-45

κ L tan −1 u = κ LP u u = 2

π 2θ D Ω hv

2

(8)

κ LP Γ

(9)

Here, u is the disorder scaling parameter, θD is the Debye temperature, Ω is the average atomic volume, h is the Planck constant, ν is the average sound velocity and Γ is the scattering parameter. The scattering parameter can be written as Γ = ΓM + ΓS, where ΓM and ΓS are scattering parameters related to mass fluctuation and strain field fluctuation, respectively. According to the theory, for the CuFe1-xInxS2 compound, the ΓM and ΓS terms can be written as 2

Fe  M In − M Fe  1 M  Γ M =  Fe  x(1 − x)  Fe  4 M  M Fe   2

 rFeIn − rFeFe  1  M Fe  ΓS =   x(1 − x)ε 2   4 M   rFe 

2

(10) 2

(11)

where M is the average atomic mass of the compound, and M Fe and rFe are the average atomic mass and radius on the Fe sublattice. Because there are two types of atoms (In and Fe) occupying sites of the Fe sublattice, then x and 1-x are the occupation fractions for In, respectively Fe on In Fe the Fe sublattice, and the atomic masses and radii are designated as M Fe / M Fe and rFIne / rFeFe ,

respectively. The relations discussed above can be expressed as In Fe M Fe = xM Fe + (1 − x ) M Fe

r Fe = xrFeIn + (1 − x ) rFeFe

(12) (13) 13



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M =

Cu M Cu + M Fe + 2 M SS 4

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(14)

Therefore, the relationship between the content of In and the scattering parameters of the CuFe1-xInxS2 compounds can be predicted based on the calculation outlined above. The results are presented in Table 2. With the increasing content of In, the scattering parameters ΓM and ΓS increase but the ΓS term is much larger than the ΓM term. This

implies that strain field

fluctuations introduced by In substitution on the Fe sublattice are the major contribution to phonon scattering and are responsible for a significantly reduced lattice thermal conductivity of CuFe1-xInxS2. As a consequence of the large decrease in the lattice thermal conductivity, the parameter (µ/κL)(m*/m0)3/2 is increased and the thermoelectric performance of all In substituted samples is much enhanced. The highest ZT value of 0.17 is achieved at 630 K with CuFe0.96In0.04S2 (shown in Figure 8(c)). This represents about 30% enhancement over that for the pristine CuFeS2 sample.

4 Conclusions In doping on sites of Fe is an effective method to reduce the lattice thermal conductivity of CuFeS2. Our study shows that, while the solid solubility of In in CuFeS2 is more than 8%, and the electronic band structure is substantially unchanged, as judged by the very small changes in the effective mass of the charge carriers. Although the presence of In in the crystal lattice of CuFeS2 decreases the carrier mobility via enhanced alloying scattering, it also weakens the influence of magnetic scattering caused by Fe3+ and, combined with a substantially reduced lattice thermal conductivity, can lead to an enhancement of the parameter (µ/κL)(m*/m0)3/2. The dominant role of In substituting for Fe is to create strain at the lattice sites which, in turn, leads to a reduction in the lattice thermal conductivity. Clearly, at present, the carrier concentration in 14


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CuFe1-xInxS2 compounds is not optimized. In future work combining doping with the formation of solid solutions and introducing nanophases into the matrix should be investigated as a promising route to improve the performance of this inexpensive and environmentally friendly material. In spite of its non-optimized transport properties, doping with In improves the thermoelectric performance of CuFeS2. The highest dimensionless thermoelectric figure of merit ZT of 0.17 was reached at 630 K for the sample with x = 0.04, an improvement of some 30% over the value of ZT of pristine CuFeS2.

Acknowledgements The authors wish to acknowledge support from the National Basic Research Program of China (973 program) under project 2013CB632502, the Natural Science Foundation of China (Grant No. 51402222, 51172174, 51521001) and the 111 Project of China(Grant No. B07040). C. U. and X. T. also acknowledge support provided by the US-China CERC-CVC program under the Award Number DE-PI0000012.

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21



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Figure 1. Crystal structures of CuFeS2 and CuInS2

Figure 2. (a) XRD patterns of PAS-sintered CuFe1-xInxS2 (x = 0, 0.02, 0.04 and 0.08); (b) The a and c lattice parameters of CuFe1-xInxS2;

22


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Figure 3. (a) (b) FESEM images of the free fracture surface of CuFe0.92In0.08S2 at different magnification. (c) BEI images of the polished surface and element maps by EDS for CuFe0.92In0.08S2.

Figure 4. The temperature dependence of (a) the electrical conductivity, (b) the Seebeck coefficient and (c) the power factor for CuFe1-xInxS2 (x = 0, 0.02, 0.04 and 0.08).

23



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Figure 5. Temperature dependence (10-300K) of (a) the carrier concentration and (b) the carrier mobility for CuFe1-xInxS2 (x = 0, 0.02, 0.04 and 0.08).

Figure 6.(a) Pisarenko plots (Seebeck coefficients as a function of carrier concentration) at room temperature. (b) Room temperature power factor (α2σ) as a function of the carrier concentration for our samples of CuFe1-xInxS2 and samples taken from the literature. The dashed lines are guides to the eyes.

24


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Figure 7. (a) Room temperature carrier mobility dependence on the alloying content for CuFeS2 compounds with different dopants (CuFe1-xInxS2, Cu1-xFe1+xS2 and Cu1-xZnxFeS2). (b) Relationship between the content of In and the calculated value of (µ/κL)(m*/m0)3/2. The dashed line is a guide to the eyes.

Figure 8. Temperature dependence of (a) the total thermal conductivity, (b) the lattice thermal conductivity and (c) the figure of merit ZT for CuFe1-xInxS2 (x = 0, 0.02, 0.04 and 0.08). The dashed line in (b) indicates the minimum thermal conductivity for CuFeS2 calculated using a model of Cahill.

25



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Samples

Composition

x=0.0

κL -1

σ -1

α

4

Page 26 of 35

µH

nH 19

-3

2

*

-1 -1

m /m0

*

(µH/κL)(m /m0)

(Wm K )

(10 S/m)

(µ µV/K)

(10 cm )

(cm V s )

Cu25.42Fe25.65S48.93

8.42

0.53

-362

4.3

9.0

2.21

3.05

x=0.02

Cu25.28Fe25.36In0.58S48.77

5.20

0.45

-358

3.5

7.6

1.92

3.91

x=0.04

Cu25.32Fe24.83In1.20S48.65

4.19

0.35

-364

3.6

6.5

1.99

4.36

x=0.08

Cu25.17Fe23.69In2.46S48.69

3.45

0.18

-382

3.3

3.4

1.96

2.73

Table 1. Room temperature transport parameters for CuFe1-xInxS2 (x = 0, 0.02, 0.04 and 0.08).

κL Compound

-1

u

Γ

ΓM

ΓS

ε2

-1

(Wm K ) CuFeS2

8.42

…

…

…

…

…

CuFe0.98In0.02S2

5.20

1.67

0.0348

0.0080

0.0268

34

CuFe0.96In0.04S2

4.19

2.23

0.0620

0.0155

0.0466

30

CuFe0.92In0.08S2

3.45

2.97

0.1096

0.0289

0.0807

26

Table 2. Disorder scattering parameters ΓM, ΓS, Γ, strain field-related adjustable parameter ε2, disorder scaling parameter u, and the calculated lattice thermal conductivity for CuFe1-xInxS2 (x = 0, 0.02, 0.04 and 0.08).

TOC 26


3/2

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Figure 1. Crystal structures of CuFeS2 and CuInS2 81x55mm (300 x 300 DPI)



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Figure 2. (a) XRD patterns of PAS-sintered CuFe1-xInxS2 (x = 0, 0.02, 0.04 and 0.08); (b) The a and c lattice parameters of CuFe1-xInxS2; 82x39mm (300 x 300 DPI)


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Figure 3. (a) (b) FESEM images of the free fracture surface of CuFe0.92In0.08S2 at different magnification. (c) BEI images of the polished surface and element maps by EDS for CuFe0.92In0.08S2. 82x62mm (300 x 300 DPI)



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Figure 4. The temperature dependence of (a) the electrical conductivity, (b) the Seebeck coefficient and (c) the power factor for CuFe1-xInxS2 (x = 0, 0.02, 0.04 and 0.08). 170x53mm (300 x 300 DPI)


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Figure 5. Temperature dependence (10-300K) of (a) the carrier concentration and (b) the carrier mobility for CuFe1-xInxS2 (x = 0, 0.02, 0.04 and 0.08). 82x40mm (300 x 300 DPI)



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Figure 6.(a) Pisarenko plots (Seebeck coefficients as a function of carrier concentration) at room temperature. (b) Room temperature power factor (α2σ) as a function of the carrier concentration for our samples of CuFe1-xInxS2 and samples taken from the literature. The dashed lines are guides to the eyes. 140x65mm (300 x 300 DPI)


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Figure 7. (a) Room temperature carrier mobility dependence on the alloying content for CuFeS2 compounds with different dopants (CuFe1-xInxS2, Cu1-xFe1+xS2 and Cu1-xZnxFeS2). (b) Relationship between the content of In and the calculated value of (µ/κL)(m*/m0)3/2. The dashed line is a guide to the eyes. 140x67mm (300 x 300 DPI)



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Figure 8. Temperature dependence of (a) the total thermal conductivity, (b) the lattice thermal conductivity and (c) the figure of merit ZT for CuFe1-xInxS2 (x = 0, 0.02, 0.04 and 0.08). The dashed line in (b) indicates the minimum thermal conductivity for CuFeS2 calculated using a model of Cahill. 170x55mm (300 x 300 DPI)


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ToC 85x39mm (300 x 300 DPI)


Nonmagnetic In Substituted CuFe1âxInxS2 Solid Solution

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Nonmagnetic In Substituted CuFe1âxInxS2 Solid Solution